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Lectures on Etale Cohomology
This book explains the following topics: Etale Morphisms, Etale Fundamental Group, The Local Ring for the Etale Topology, Sheaves for the Etale Topology, Direct and Inverse Images of Sheaves, Cohomology: Definition and the Basic Properties, Cohomology of Curves, Cohomological Dimension, Purity; the Gysin Sequence, The Proper Base Change Theorem, Cohomology Groups with Compact Support, The Smooth Base Change Theorem, The Comparison Theorem, The Kunneth Formula, Proof of the Weil Conjectures, The Weil Conjectures, The Geometry of Lefschetz Pencils and Cohomology of Lefschetz Pencils.
Author(s): J.S. Milne
202 Pages 
Lectures notes in universal algebraic geometry
This note contains below topics, Algebraic structures, Subalgebras direct products homomorphisms, Simplifications of terms, Equations and solutions, Algebraic sets and radicals, Equationally Noetherian algebras, Coordinate algebras, Main problems of universal algebraic geometry, Properties of coordinate algebras, Coordinate algebras of irreducible algebraic sets, When all algebraic sets are irreducible, The intervention of model theory, Geometrical equivalence, Unifying theorems, Appearances of constants, Coordinate algebras with constants.
Author(s): A. Shevlyakov
67 Pages
Lecture Notes on Multi loop Integral Reduction and Applied Algebraic Geometry
These notes are for lectures on integral reduction and applied algebraic geometry techniques, given at a school on amplitudes in Beijing in 2016. They show how algebraic geometry is used to reduce multiloop integrals.
Author(s): Yang Zhang
92 Pages
Seven Lectures on the Universal Algebraic Geometry
This note contains below topics, What is the Universal Algebraic Geometry Lecture, Algebraic sets and algebraic varieties Lecture, Geometric properties and geometric relations of algebras Lecture, Algebraic geometry in groupbased algebras Lecture, Isomorphisms of categories of algebraic sets Lecture, Algebraic geometry in the First Order Logic FOL Lecture, Generic view, Some information from universal algebra, Algebras with a fixed algebra of constants, Systems of equations and algebraic sets, Lattices of algebraic sets, Categories of algebraic sets.
Author(s): Boris Plotkin
87 Pages
An introduction to derived algebraic geometry
This book contains below topics, Introduction and dgalgebras, Infinity categories and model categories, Consequences for dgalgebras, Simplicial structures, Geometric nstacks, Derived geometric nstacks.
Author(s): J. Eugster, J. P. Pridham
100 Pages
This note contains below topics, Examples of homogeneous varieties, Auxilliary varieties, Topology and consequences, Projective dierential invariants, Varieties with degenerate Gauss images, When can a uniruled variety be smooth, Dual varieties, Linear systems of bounded and constant rank, Secant and tangential varieties, Systems of quadrics with tangential defects, Recognizing uniruled varieties.
Author(s): Joseph M. Landsberg
70 Pages
This note contains below topics, Preliminary Material, Lelong Numbers and Intersection Theory, Holomorphic Vector Bundles, Connections and Curvature, Bochner Technique and Vanishing Theorems, Numerically Eective Line Bundles, Seshadri Constants and the Fujita Conjecture, Algebraic Approach of the Fujita Conjecture, Regularization of Currents and Selfintersection Inequ alities, Use of MongeAmp ere Equations, Numerical Criteria for Very Ample Line Bundles, Holomorphic Morse Inequalities.
Author(s): Jean-Pierre Demailly
95 Pages
Introduction to Algebraic Geometry by JustinRSmith
This note covers classical result, Affine varieties, Local properties of affine varieties, Varieties and Schemes, Projective varieties and Curves.
Author(s): JustinR.Smith
663 Pages
Algebraic Geometry I Lecture Notes Roman Bezrukavnikov
The contents of this book include, Course Introduction, Zariski topology, Affine Varieties, Projective Varieties, Noether Normalization, Grassmannians, Finite and Affine Morphisms, More on Finite Morphisms and Irreducible Varieties, Function Field, Dominant Maps, Product of Varieties, Separateness, Sheaf Functors and Quasicoherent Sheaves, Quasicoherent and Coherent Sheaves, Invertible Sheaves, Quasi coherent sheaves on Projective Spaces, Divisors and the Picard Group, Bezouts Theorem, AbelJacobi Map, Elliptic Curves, KSmoothness, Canonical Bundles, the Adjunction Formulaahler Differentials, Cotangent Bundles of Grassmannians, Bertinis Theorem, Coherent Sheves on Curves, Derived Functors, Existence of Sheaf Cohomology, BirkhoffGrothendieck, RiemannRoch, Serre Duality, Proof of Serre Duality.
Author(s): Roman Bezrukavnikov
63 Pages